$\left\{\begin{array} { l } 25x+15y=35 \\ 4x+5y=3\end{array} \right.$
Multiply both sides of the equation by $-3$$\left\{\begin{array} { l } 25x+15y=35 \\ -12x-15y=-9\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$13x=26$
Divide both sides of the equation by $13$$x=2$
Substitute the given value of $x$ into the equation $4x+5y=3$$4 \times 2+5y=3$
Solve the equation for $y$$y=-1$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 2, -1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 5 \times 2+3 \times \left( -1 \right)=7 \\ 4 \times 2+5 \times \left( -1 \right)=3\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 7=7 \\ 3=3\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 2, -1\right)$